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Simplifying 12x2 + -44x + 22 = 0 Reorder the terms: 22 + -44x + 12x2 = 0 Solving 22 + -44x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -22x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -22x + 6x2)' equal to zero and attempt to solve: Simplifying 11 + -22x + 6x2 = 0 Solving 11 + -22x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -3.666666667x + -1.833333333 + x2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -3.666666667x + x2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + -1.833333333 -3.666666667x + x2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 -3.666666667x + x2 = -1.833333333 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = -1.833333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = -1.833333333 + 3.361111114 Combine like terms: -1.833333333 + 3.361111114 = 1.527777781 3.361111114 + -3.666666667x + x2 = 1.527777781 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 1.527777781 Calculate the square root of the right side: 1.236033082 Break this problem into two subproblems by setting (x + -1.833333334) equal to 1.236033082 and -1.236033082.Subproblem 1
x + -1.833333334 = 1.236033082 Simplifying x + -1.833333334 = 1.236033082 Reorder the terms: -1.833333334 + x = 1.236033082 Solving -1.833333334 + x = 1.236033082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 1.236033082 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 1.236033082 + 1.833333334 x = 1.236033082 + 1.833333334 Combine like terms: 1.236033082 + 1.833333334 = 3.069366416 x = 3.069366416 Simplifying x = 3.069366416Subproblem 2
x + -1.833333334 = -1.236033082 Simplifying x + -1.833333334 = -1.236033082 Reorder the terms: -1.833333334 + x = -1.236033082 Solving -1.833333334 + x = -1.236033082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -1.236033082 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -1.236033082 + 1.833333334 x = -1.236033082 + 1.833333334 Combine like terms: -1.236033082 + 1.833333334 = 0.597300252 x = 0.597300252 Simplifying x = 0.597300252Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.069366416, 0.597300252}Solution
x = {3.069366416, 0.597300252}
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